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Physics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 3 · Q28
A potential difference of 1.0 V is applied across a conductor of length 5.0 m and area of cross-section 1.0 mm^2. When current of 4.25 A is passed…
A potential difference of $\displaystyle 1.0$ V is applied across a conductor of length $\displaystyle 5.0$ m and area of cross-section $\displaystyle 1.0 \mathrm{~mm}^{2}$. When current of $\displaystyle 4.25$ A is passed through the conductor, calculate
(i)
the drift speed and (ii) relaxation time, of electrons. (Given number density of electrons in the conductor, $\displaystyle \mathrm{n}=8.5 \times 10^{28} \mathrm{~m}^{-3}$ ).
Marking-scheme solution
(i)
$\displaystyle v_{d}=\frac{I}{e n A}$
$\displaystyle =\frac{4.25}{1.6 \times 10^{-19} \times 8.5 \times 10^{28} \times 10^{-6}} \mathrm{~m} / \mathrm{s}$
$\displaystyle =3.125 \times 10^{-4} \mathrm{~m} / \mathrm{s}$
(ii)
$\displaystyle \tau=\frac{v_{d} m l}{e V}$
$\displaystyle =\frac{3.125 \times 10^{-4} \times 9.1 \times 10^{-31} \times 5}{1.6 \times 10^{-19} \times 1}$
$\displaystyle =88.72 \times 10^{-16} \mathrm{~s}$
$\displaystyle =8.872 \times 10^{-15} \mathrm{~s}$
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